Tests for nonrandomness in quantum jumps

Abstract

In a fundamental test of quantum mechanics, we have observed 228 000 quantum jumps of a single trapped and laser cooled 88 Sr + ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be Ͻ6.5ϫ 10 −4 when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze 238 000 quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short-or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.An axiom of quantum mechanics is that we cannot predict the result of any single measurement of an observable of a quantum-mechanical system in a superposition of eigenstates. Testing this principle is important, not only for basic science, but also for applications such as quantum random number generators (QRNG's) and potential quantum computers. It is therefore surprising that in spite of the many experiments sensitive to quantum-mechanical effects, only a few experiments have explicitly searched for nonrandom behavior in long sequences of repeated quantum measurements. In Refs. [1,2], the randomness of the path of a single photon after a beam splitter was used to build QRNG's. In Ref.[3], the arrival times of decay products of unstable nuclei were used to test the statistics of quantum decay. Although both these systems rapidly give excellent statistics, detector inefficiencies limit the conclusions that can be drawn regarding the unpredictability of quantum-mechanical measurements. Furthermore, both systems are insensitive to certain types of nonrandom behavior: averaging over many particles in a collection of nuclei could obscure nonrandom behavior of single systems; patterns in emission times or photon arrival times could be overlooked because of inefficient detectors, and because beam splitters are always somewhat biased, QRNG's based on them are designed to be insensitive to consecutive runs of transmissions or reflections. All these problems can be avoided by observing the times of quantum jumps in a single atom [4] because transitions between atomic levels can be detected with near-unit efficiency with no multiparticle effects [5].Here, we analyze the intervals between quantum jumps of a trapped ion and answer the question "after we h...

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